How to Make It
Using a very sharp knife, thinly slice the beef 1/8 inch thick, then cut into 3/4-inch-thick strips. In a medium bowl, toss the meat with 1/2 teaspoon of salt to coat. Let stand at room temperature for 30 minutes.
In a large skillet, heat 2 tablespoons of the oil. Add the garlic; cook over moderate heat, stirring, for 1 minute. Add the tomatoes and cook, stirring occasionally, until they soften and start to split open, about 3 minutes. Transfer to a medium bowl. Wipe out the skillet.
In the same skillet, heat the remaining 2 tablespoons of olive oil. Add the beef strips and cook over high heat, stirring occasionally, until browned in spots, about 1 minute. Stir in the vinegar and cook until no trace of pink remains, about 2 minutes longer. Transfer the meat and any juices to shallow bowls and top with the tomatoes and arugula. Garnish with cheese shavings and serve.